Textbook in PDF format

This textbook takes physics and engineering undergraduates through the mathematics they need in the first years of study. It offers an accessible approach which is characterized by the combination of the textbook with a detailed study guide. This study guide, supplied as freely accessible downloads for each chapter, divides the whole learning task into small units. You will read and study a limited section of the textbook and then return to the study guide afterwards. Learning results are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. The degree of difficulty slowly rises, which will let you gain confidence and experience your own progress, thus fostering motivation. The sequence of studies can be individualized according to performance and can be regarded as a full tutorial course. This combination of a textbook with a detailed study guide is a powerful means to meet the rising importance of learning outside of lectures at home and will be of great benefit, especially to students learning remotely.
The most important change in this third edition is a much tighter connection between the textbook and the accompanying study guide. We included more detailed suggestions for the sequence and use of the material in the study guide. Now the textbook refers directly to the corresponding page in the study guide after each little chunk of material. This will be of great benefit, especially to students learning remotely. This third edition is extended with new topics including, among others, the plane in higher dimensional space, the scalar triple product, and power series of the cosine. Some formal errors have been corrected, and the index has been improved